Consider a large macro-electrode, about 1 cm in diameter. The diffusion at its edge is negligible and the flux over its surface can be considered homogeneous. Therefore you can use the 1D diffusion equation to simulate its behavior. This Demonstration shows the concentration profile over the surface of a macro-electrode as a function of the diffusion coefficient and time.
The diffusion equation for a macro-electrode in one spatial dimension is given by
,
where is the diffusion coefficient (/s) and is the concentration at distance at time .
The boundary conditions are:
at , ;
as , ;
at , .
The analytical solution is given by .
As the diffusion coefficient increases, the speed of the diffusion increases. As time increases, the concentration approaches a nearly steady-state condition.
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